The old official numbering system was, ala, wan, tu, mute, or a the limited roman style This was a roman system, e.g. W, T, TW, TT, TTW, TTT, TTTW, etc. A ternary place value system would have been better, but just as verbose.
The official number system is a Roman style number system. I sort of like it when written in Roman style, but only when written, and only for numbers up to about 159. After 159, the length of the numbers starts to get unbearably long.
The don’t do math option.
This option is good up unto the point where you decide to translate anything of substance, eventually years will come up. It’s even possible famous equations will come up, like e=mc^2. Doubly so for non-fiction.
I recommend using wan, tu, mute when you are not in the mood for numbers. Use roman-style for numbers up to 160 or so, but when you aren’t doing math. And for all other numbers, establish a system within your text and then uses it. If I was going to invent a new kind of algebra, I might need to create a new notation. But once described, I’d be able to use it, using English, and no one would accuse me of re-plumbing English. I think the situation is the same for constructed languages where the designer didn’t bother to work out the full number system. And why should they? Each language designer designs a language for their own goals, and that is a good thing.
Options for Digits
- Assign base words with a vague sense of quantity to specific numbers.
In fact, this is the current state of affairs.
A color system either reuses the electrical resistor number system, or the colors from ROYGBIV scale are mapped to decimal digits.
- Body Parts
Papa New Guinean natives will count along an imaginary line along their body. For example nose could be one, lips two, chin three, etc.
- Load words
I don’t really like loan words for small vocabulary languages. Each loan word is a new word and increases the number of words a brand new user need to memorize before getting started. (Finishing learning a language will still require memorizing 1,000s of lexemes, but that is another blog post)
- Calender names. Days can provide numbers from 1 to 7, Months 1 to 12. Month could support decimal if we ignore two months.
There is a perfectly good proposal to use Japanese style day names.
Options for reading off the digits and symbols
- Grammatical sentences
This encourages awkward spoken mathematical notation. It would be better to just read off the symbols as they appear. Trying to shoe-horn mathematical notation into a constructed language using the language’s internal grammar is like saying phone number as “first there is an 9, then there is a 7, then there is a 9, etc.” 555-234-2344 is just fine without verbs, without trying to get it to follow any rules about agreement.
- Use Calques and descriptive words for symbols.
- Decimal places are circular things. But exponents are pretty abstract. I’m thinking the odds of finding a short-transparent compound phrase are fairly low. More over, notation should be somewhat brief to read. So this all favors choosing non-transparent words. If there isn’t a good short word for factorial, might as well use “kala”. At least “kala” won’t likely be misunderstood for “fish”. Normally “tu” would be a good verb for divide, but because it also is a digit, it would be a lousy name for an operator.
Good properties of number systems for toki pona like languages
1) Don’t use loan words. If you’re going to use loan words, why not speak Esperanto?
2) Use decimal, unless you’re just doing a number system for show.
3) Don’t re-invent the wheel. Numbers are only kind of linguistic entities and mathematical notation is not linguistic at all. Don’t bother creating a syntax and grammar for reading off mathematical notation or invent a new mathematical notation. Unless you are doing so for show.